He started to study microbiology, but then moved into physics and maths, graduating with a Bachelor of Science degree at the University of the Witwatersrand Johannesburg. He studied physics and obtained his Master of Science degree at the University of Cape Town. He was awarded an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851, which enabled him to move to England, completing his PhD in research physics at Trinity College, Cambridge in 1953.
Following his PhD, Klug moved to Birkbeck College in the University of London in late 1953, and started working with virologist Rosalind Franklin in the lab of crystallographer John Bernal. This experience aroused a lifelong interest in the study of viruses, and during his time there he made discoveries in the structure of the tobacco mosaic virus. In 1962 he moved to the newly built Medical Research Council (MRC) Laboratory of Molecular Biology (LMB) in Cambridge. Over the following decade Klug used methods from X-ray diffraction, microscopy and structural modelling to develop crystallographic electron microscopy in which a sequence of two-dimensional images of crystals taken from different angles are combined to produce three-dimensional images of the target. He studied the structure of transfer RNA, and found what is known as zinc fingers as well as the neurofibrils in Alzheimer's disease.